Answers
The change of base formula states that:
[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.
In this case we have:
[tex]\begin{gathered} x=14 \\ b=\sqrt[]{3} \end{gathered}[/tex]Then, using the change of base formula, we have:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln 14}{\ln \sqrt[]{3}}[/tex]Once we have the expression we just evaluate the expression on the right to get the appoximation we need:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln14}{\ln\sqrt[]{3}}\approx4.804[/tex]Related Questions
Question is attached in photo Function : f(x)=x+2 sin x
Answers
Answer:
The function is given below as
[tex]f(x)=x+2\sin x[/tex]Using the interval below
[tex]0\leq x\leq2\pi[/tex]A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph).
Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).
Using a graphing tool, we will have the relative maximum and relative minimum to be
Hence,
The relative maximum is at
[tex](\frac{2\pi}{3},3.826)[/tex]The relative minimum is at
[tex](\frac{4\pi}{3},2.457)[/tex]which of the following describe ✓2) Irrational number) Whole number ) Integer) Real number
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Okay, here we have this:
Considering that a real number is said to be irrational if it cannot be expressed as a quotient of whole numbers. ✓2 is an irrational number, and as all the irrational number are real numbers ✓2 is also a real number.
Evaluate the following definite integral using a geometric formula. You must show all work including the geometry area formula .
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Given the Definite Integral:
[tex]\int_0^1\sqrt{1-x^2}dx[/tex]You can identify that the interval is:
[tex]\lbrack0,1\rbrack[/tex]By definition, if the function is continuous and positive in a closed interval, then:
[tex]\int_a^bf(x)dx=Area[/tex]In this case, you can identify that the function is:
[tex]y=\sqrt{1-x^2}[/tex]You can graph it using a graphic tool:
Since the closed interval goes from 0 to 1, you need to find this area:
You can identify that you have to find the area of a quarter circle. In order to do it, you can use this formula:
[tex]A=\frac{\pi r^2}{4}[/tex]Where "r" is the radius of the circle.
In this case, you can identify that:
[tex]r=1[/tex]Therefore, you get:
[tex]A=\frac{\pi(1)^2}{4}=\frac{\pi}{4}[/tex]Then:
[tex]\int_0^1\sqrt{1-x^2}dx=\frac{\pi}{4}[/tex]Hence, the answer is: Option D.
There are 11 oranges, 7 apples, 9 bananas and 13 peaches in the fruit bowl. If you pick a fruit at random, what is the probability you will pick an apple or banana? (give answer as a percentage rounded to the nearest tenth) Plapple or banana)=[answer]
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we get that:
[tex]\frac{7+9}{11+7+9+13}=\frac{16}{40}=\frac{2}{5}=0.4\rightarrow40\text{ \%}[/tex]What value of Y makes this equation true?6y/-2 = 8 (-4/2)
Answers
Step 1
Given;
[tex]\frac{6y}{-2}=8(-\frac{4}{2})[/tex]Required; To find the value of y that makes the equation true
Step 2
Find the value of y
[tex]\begin{gathered} \text{Simplify} \\ -3y=4(-4) \end{gathered}[/tex][tex]\begin{gathered} \text{expand} \\ -3y=-16 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by -3} \\ \frac{-3y}{-3}=\frac{-16}{-3} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplify} \\ y=\frac{16}{3} \end{gathered}[/tex]Hence, the value of y that makes the equation true is 16/3
sin(theta) = .754
What is theta
Answers
Answer: I believe it is representing the angular position of a vector
In short, it is a symbol to represent a measured angle.
A storm is moving at 30km/hr .it is 60 km away. What time will it arrive
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From the information provided, the storm is travelling at a speed of 30km/hr. In other words, its travelling 30 kilometers every hour. If the storm is 60 kilometers away, then we have the following ratio;
[tex]undefined[/tex]Which of the following actions will best help her find out whether the two equations in the system are in fact parallel
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Check to see whether the slope of both lines are the same (option A)
Explanation:[tex]\begin{gathered} \text{Given} \\ y\text{ - x = }21 \\ 2y\text{ = 2x + 16} \end{gathered}[/tex]When two system of equations do not intersect, the lines are said to be parallel lines.
This means there is no solution.
To determine if the lines are trully parallel, the slope of each equation need to be determined.
For parallel lines, the slope will be the same
The best action to help her find out whether the two equations are inded parallel, Check to see whether the slope of both lines are the same (option A)
please show me how to solve this triangle, thank you!
Answers
Statement Problem: Solve for the missing sides of the triangle;
Solution:
The sum of angles in a triangle is 180degrees. Thus,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle B=180^o-\angle A-\angle C \\ \angle B=180^o-42^o-96^o \\ \angle B=42^o \end{gathered}[/tex]Since measure angle A and measure angle B are equal. Thus, the triangle is isosceles and the two sides are equal.
[tex]a=b[/tex]We would apply sine rule to find the missing side a.
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin A}{a}=\frac{\sin C}{c} \end{gathered}[/tex][tex]\begin{gathered} \frac{\sin42^o}{a}=\frac{\sin96^o}{12} \\ a=\frac{12\sin42^o}{\sin96^o} \\ a=8.07 \\ a\approx8.1 \end{gathered}[/tex]Thus,
[tex]a=b=8.1[/tex]CORRECT ANSWERS:
[tex]\begin{gathered} a=8.1 \\ b=8.1 \\ m\angle B=42^o \end{gathered}[/tex]give the quadratic function a graph for the function f (x)= -(x-3)^2-2
Answers
Answer
The graph of the function f(x) = -(x - 3)² - 2, is presented below
Explanation
We are told to graph a given function
f(x) = -(x - 3)² - 2
The first step into making this easy is to open the bracket.
f(x) = - (x² - 6x + 9) - 2
f(x) = -x² + 6x - 9 - 2
f(x) = -x² + 6x - 11
The next step is then to insert different values of x into the function and obtain the corresponding value of the function. This set of ordered pairs arethen plotted to form the graph.
The graph is then plotted and presented under 'Answers' above.
Hope this Helps!!!
Can a triangle be formed with side lengths 13, 7, and 5? Explain.
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Answer: The answer is no
Step-by-step explanation:
this is because the two short side lengths, which is 5 and 7, they have to be added together, which is 12, and 12 is smaller than 13 (the largest side)
Answer:
No, because 5 + 7 < 13
Step-by-step explanation:
Find the (x , y) coordinate(s) of any hole(s) in h( x ). If there is none, write “n/a”.Round to two decimals.
Answers
The hole appears in the rational function when the numerator and the denominator have the same zeroes
Since the rational function is
[tex]h(x)=\frac{x+7}{x^2-49}[/tex]Factorize the denominator
[tex]x^2-49=(x+7)(x-7)[/tex]The rational function h(x) is
[tex]h(x)=\frac{x+7}{(x+7)(x-7)}[/tex]Since (x + 7) is in both numerator and denominator
Then there is a hole at x + 7 = 0
Let us find the value of x
[tex]\begin{gathered} x+7=0 \\ x+7-7=0-7 \\ x=-7 \end{gathered}[/tex]The whole is at x = -7
Then simplify the fraction to find the value of y at x = -7
[tex]h(x)=\frac{(x+7)}{(x+7)(x-7)}[/tex]Cancel the bracket (x+7) up by the same bracket down
[tex]h(x)=\frac{1}{x-7}[/tex]Substitute x by -7
[tex]\begin{gathered} h(-7)=\frac{1}{-7-7} \\ h(-7)=\frac{1}{-14} \\ y=-\frac{1}{14} \end{gathered}[/tex]The hole is at (-7, -1/14)
A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let x be the number of 40-pound boxes and y be the number of 65-pound boxes. The forklift can carry up to either 45 boxes or a weight of 2,400 pounds. Which of the following systems of inequalities represents this relationship? 40x + 657 $ 2.400 rty < 45 C) | 40r + 657 $ 45 | x + y < 2.400 B) [xu y < 2.100 40x + 657 $ 2.400 xl y < 1
Answers
Let:
x = number of 40-pound boxes
y = number of 65-pound boxes
The forklift can carry up to either 45 boxes
This means:
[tex]x+y\leq45[/tex]The forklift can carry up a weight of 2,400 pounds:
This means:
[tex]40x+65y\leq2400[/tex]Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
Answers
Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
1)
we have
100%-22%=78%=78/100=0.78
so
If is discounted 22%
the new price is 100,000*0.78=$78,000
2) If it is then marked up 22%
the new price is
100%+22%=122%=122/100=1.22
78,000*1.22=$95,160
therefore
The new price is not $100,000
the new price is $95,160
Quadrilateral ABCD with vertices A(0,7) B(1,3), C(-1,-4), and D(-5,1): <7,-3>
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We will have the following:
2)
A(0, 7) : <7, -3>
[tex]A^{\prime}(7,4)[/tex]B(1, 3) : <7, -3>
[tex]B^{\prime}(8,0)[/tex]C(-1, -4) : <7, -3>
[tex]C^{\prime}(6,-7)[/tex]D(-5, 1) : <7, -3>
[tex]D^{\prime}(2,-2)[/tex]3)
From the graph we will have the following:
a.
[tex](x,y)\to(x+7,y+5)[/tex]b.
[tex]\langle7,5\rangle[/tex]***Explanation***
For point 2, we will simply apply the vector to the corresponding coordinates, that is:
We have the coordinates:
[tex]A(a,b)[/tex]and the vector:
[tex]\langle c,d\rangle[/tex]So, in order to determine the final image we will have to follow the transformation rule:
[tex]A^{\prime}(a+c,b+d)[/tex]*For point 3, we will simply count the number of units the image has moved to the left or rigth and that will be our transformation rule for the x-axis, and the number of units the image has moved up or down and that will be our transformation rule for the y-axis.
In the case of the problem, the images moved 7 units to the rigth (+7) and then moved 5 units up (+5), so the transformation rule in coordinate notation is given by:
[tex](x,y)\to(x+7,y+5)[/tex]And in order to write it in vector notation, we simply write the units the images move:
[tex]\langle7,5\rangle[/tex]The current population of a threatened animal species is 1.3 million, but it is declining with a half-life of 25 years. How many animals will be left in 35 years? in 80 years?Question content area bottom(Round to the nearest whole number as needed.)
Answers
Given:
it is given that the current population of a threatened animal species is 1.3 million, but it is declining with a half-life of 25 years.
Find:
we have to find that how many animals will be left in 35 years and in 80 years.
Explanation:
we know 1.3million = 1300000
The decay law is
[tex]P(t)=1300000\times(\frac{1}{2})^{\frac{t}{25}}[/tex]
where t is in years and p(t) is the population at time t.
Now, the number of animals left in 35 years is
[tex]\begin{gathered} P(35)=1300000\times(\frac{1}{2})^{\frac{35}{25}} \\ P(35)=1300000\times(\frac{1}{2})^{1.4} \\ P(35)=492608(by\text{ rounded to nearest whole number\rparen} \end{gathered}[/tex]Therefore, 492608 animals will be left in 30 years.
Now, the number of elements left in 80 years is
[tex]\begin{gathered} P(80)=1300000\times(\frac{1}{2})^{\frac{80}{25}} \\ P(80)=1300000\times(\frac{1}{2})^{3.2} \\ P(80)=141464(by\text{ rounded to nearest whole number\rparen} \end{gathered}[/tex]Benjamin & Associates, a real estate developer, recently built 194 condominiums in McCall, Idaho. The condos were either two-bedroom units or three-bedroom units. If the total number of rooms in the entire complex is 494, how many two-bedroom units are there? How many three-bedroom units are there
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x = number of 2 bedrooms units
y= number of 3 bedroom units
194 condominiums
x+y = 194 (a)
the total number of rooms in the entire complex is 494
2x + 3y = 494 (b)
We have the system of equations:
x+y = 194 (a)
2x + 3y = 494 (b)
Solve (a) for x
x = 194-y
Replace x on (b) and solve for y
2 (194-y ) + 3 y = 494
388 - 2y +3 y = 494
-2y+3y = 494-388
y= 106
Replace y on (a) and solve for x
x + 106 = 194
x = 194-106
x= 88
2-bedroom units = 88
3- bedrooms units = 106
Elena has two aquariums each shaped like a rectangular prism. For each question explain or show your reasoning. A) One aquarium has a length of 7/2 feet a width of 4/3 feet and a height of 3/2 feet. What is the volume of the aquarium.
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Select the correct location on the image. Click the digit in the hundred millions place. 7,7 7 8,7 6 8,2 4.9 Reset Next
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In this case you need to click the 7 which is in the hundred millions place
You pick a card at random.
1 2 3 4
What is P(factor of 24)?
Write your answer as a percentage rounded to the nearest tenth
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Answer:
100%
Step-by-step explanation:
All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.
This is equal to 100%.
help meeeee pleaseeeee!!!
thank you
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The values of the given polynomial are:-
f(0) = 12
f(2) = 28
f(-2) = 52
Given polynomial:-
[tex]f(x)=-x^3+7x^2-2x+12[/tex]
We have to find the values of f(0), f(2) and f(-2).
Putting x = 0 in f(x), we get,
[tex]f(0)=-(0)^3+7(0)^2-2(0)+12[/tex]
f(0) = 0 +0 - 0 + 12 = 12
Hence, the value of f(0) is 12.
Putting x = 2 in f(x), we get,
[tex]f(2)=-(2)^3+7(2)^2-2(2)+12[/tex]
f(2) = -8 + 28 - 4 + 12 = 28
Hence, the value of f(2) is 28.
Putting x = -2 in f(x), we get,
[tex]f(-2)=-(-2)^3+7(-2)^2-2(-2)+12[/tex]
f(-2) = 8 +28 + 4 +12 = 52
Hence, the value of f(-2) is 52.
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Describe the difference on table, graph and equation between discrete and continuous functions.
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REmember that
A continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values
A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers.
Discrete functions have scatter plots as graphs and continuous functions have lines or curves as graphs
2/4 turn into decimal
Answers
Answer:
The decimal form of 2/4 is;
[tex]0.5[/tex]Explanation:
We want to turn the fraction to decimal.
[tex]\frac{2}{4}=0.5[/tex]it can be obtained by;
Therefore, the decimal form of 2/4 is;
[tex]0.5[/tex]What is the value of the x variable in the solution to the following system ofequations? (5 points)4x - 3y = 35x - 4y = 3O x can be any number as there are infinitely many solutions to this systemThere is no x value as there is no solution to this systemO-303
Answers
Step 1:
Write the two systems of equations
4x - 3y = 3
5x - 4y = 3
Step 2:
Use the elimination method to eliminate y.
[tex]\begin{gathered} 4x\text{ - 3y = 3} \\ 5x\text{ - 4y = 3} \\ \text{Use the elimination method to eliminate y} \\ 4x\text{ - 3y = 3 }\times\text{ 4} \\ 5x\text{ - 4y = 3 }\times\text{ 3} \\ 16x\text{ - 12y = 12} \\ 15x\text{ - 12y = 9} \\ 16x\text{ - 15x = 12 - 3} \\ \text{ x = 3} \end{gathered}[/tex]Final answer
x = 3
Question 12 pls help
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The equation of the line is found as y + 2 = (-2/3)(x - 5).
What is termed as the equation of a line?The equation of line is just an algebraic representation of a set of points in a coordinate system that form a line. The numerous points in the coordinate axis that form a line are depicted as a set of factors x, y to form an algebraic expression known as an equation of a line.For the given question.
The passing coordinates of the line is given as;
(x1, y1) = (-1, 7)
(x2, y2) = (5, -2)
Find the slope using the equation.
slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (-2 - 7)/(5 + 1)
m = -9/6
m = -3/2
Use the point slope formula to find the equation of line in slope intercept form.
y - y1 = m(x - x1)
y + 2 = (-2/3)(x - 5)
Thus, the equation of the line is found as y + 2 = (-2/3)(x - 5).
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Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
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Based on the fact that Home Liquidators marked up their merchandise by 35% on cost, the company equivalent markup on selling price is 26%.
How to find the equivalent markup?The equivalent markup by Home Liquidators on the selling price can be found by the formula:
= Percentage markup / Percentage selling price x 100%
The percentage markup = 35%
Percentage selling price = (100% + 35%) = 135%
The equivalent markup by Home Liquidators is therefore:
= 35% / 135% x 100%
= 26%
In conclusion, the Home Liquidators has an equivalent markup of 26% on selling price.
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Which fraction is less than 3/5 is it 5/7, 9/15, 4/6, 7/12
Answers
Answer: 7/12
Step-by-step explanation:
3/5=0.6
5/7=0.71428571428
9/15=0.6
4/6=0.66666
7/12=0.583333
Answer: 7/12
Step-by-step explanation:
I have attached my work.
Solve x4 + 8x2 + 15 = 0.X = +15 and x = 113x = 5 and x = 13x = 113 and x = 15X = 3/1/3 and x = 1115
Answers
Answer
Option D is correct.
x = ±i√(5) OR ±i√(3)
Explanation
The question wants us to solve
x⁴ + 8x² + 15 = 0
To solve this, we first say that
Let x² = y
So that,
x⁴ = (x²)² = y²
So, the equation becomes
y² + 8y + 15 = 0
This is a simple quadratic equation, we then solve this
y² + 8y + 15 = 0
y² + 3y + 5y + 15 = 0
y (y + 3) + 5 (y + 3) = 0
(y + 5) (y + 3) = 0
y + 5 = 0 OR y + 3 = 0
y = -5 OR y = -3
But, Recall that x² = y
If y = -5
x² = y = -5
x² = -5
x = √(-5)
If y = -3
x² = y = -3
x² = -3
x = √(-3)
So,
x = √(-5) OR x = √(-3)
Note that
√(-1) = i
√(-5) = √(-1) × √(5)
= i√5
And
√(-3) = √(-1) × √(3)
= i√3
Hence
x = ±i√(5) OR ±i√(3)
Hope this Helps!!!
The two angles shown are supplementary.162°Which equation can be solved to find the value of x, and what is the value of x?A.162° + Xo = 90°; x = 72B.162° + x° = 180°; x = 18C.162° + x = 360°; x= 198D.162° + x = 180°; x = 242
Answers
Supplementary angles are two angles whose sum is exactly 180, therefore:
162 + x = 180
Solving for x:
subtract 162 from both sides:
x = 180 - 162
x = 18
I need help This is from my trig prep guide
Answers
From the question given, we have the following data;
Height of the tree = 80 feet
Angle of elevation to the top of the tree = 68 degrees
Distance from Corey to the tree = unknown
We shall now call the unknown variable x.
With that we shall have the following diagram;
We now have a diagram detailing the triangle and the dimensions showing Corey, the tree and the eagle at the tree top.
To get a better look, Corey moves several steps away from the tree and now determines his new angle of elevation to be 41 degrees.
This can now be illustrated as follows;
From triangle EDC, we shall calculate the distance from point C to point D using trigonometric ratios. The reference angle is at point C, which means the opposite side is side ED. The adjacent side is side CD (labeled x). Using trig ratios we have;
[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 68=\frac{80}{x} \end{gathered}[/tex]We cross multiply and we now have;
[tex]\begin{gathered} x=\frac{80}{\tan 68} \\ U\sin g\text{ a calculator, we have tan 68 as 2.475086}\ldots \\ x=\frac{80}{2.475086} \\ x=32.322109\ldots \\ \text{Rounded to the nearest hundredth of a foot;} \\ x=32.32ft \end{gathered}[/tex]Looking at triangle EDB;
The reference angle is 41 which makes the opposite side ED and the adjacent side BD. To calculate the distance BD, we'll have;
[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 41=\frac{80}{BD} \\ We\text{ cross multiply and we now have;} \\ BD=\frac{80}{\tan 41} \\ BD=\frac{80}{0.869286} \\ BD=92.02955\ldots \\ \text{Rounded to the nearest hundredth;} \\ BD=92.03 \end{gathered}[/tex]Take note that the distance Corey moved before he had a new angle of elevation is line segment CD which is indicated as y. Note also that
[tex]\begin{gathered} BC+CD=BD \\ CD=x=32.32ft \\ BC+32.32=92.03 \\ \text{Subtract 32.32 from both sides;} \\ BC=59.71 \end{gathered}[/tex]The distance Corey stepped back is indicated as y (line segment BC).
ANSWER:
Corey stepped back 59.71 feet